Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and information management, (2) combined situation and impact assessment, and (2) knowledge representation between machine processing and user coordination. Various applications leverage DSmT “Advances” listed above along with DSmH (hybrid), DSmP (Probabilistic), and DSmT theoretical insights. The third volume attacks these application issues of coordination between the “levels” of information fusion....

Part I Advances on DSmT 1 Chapter 1 An introduction to DSmT 3 by J. Dezert and F. Smarandache 1.1 Introduction . . . . . . . . . . 4 1.2 Foundations of DSmT . . . . . . . . . 4 1.2.1 The power set, hyper-power set and super-power set . . 6 1.2.2 Notion of free and hybrid DSm models . . . . 18 1.2.3 Generalized belief functions . . . . . . 20 1.2.4 The classic DSm rule of combination . . . . . 21 1.2.5 The hybrid DSm rule of combination . . . . . 22 1.2.6 Examples of combination rules . . . . . . 24 1.2.7 Fusion of imprecise beliefs . . . . . . 29 1.3 Proportional Conflict Redistribution rule . . . . . 33 1.3.1 PCR formulas . . . . . . . . . 34 1.3.2 Examples . . . . . . . . . 35 1.3.3 Zadeh’s example . . . . . . . . 39 1.4 Uniform and partially uniform redistribution rules . . . 41 1.5 RSC Fusion rules . . . . . . . . . 43 1.6 The generalized pignistic transformation (GPT) . . . . 45 1.6.1 The classical pignistic transformation . . . . 45 1.6.2 Notion of DSmcardinality . . . . . . 46 1.6.3 The Generalized Pignistic Transformation . . . 47 1.7 The DSmP transformation . . . . . . . 48 1.7.1 The Probabilistic In...

This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigations while, Part 2 presents several applications of this new theory. Some ideas in this book are still under current development or improvements, but we think it is important to propose them in order to share ideas and motivate new debates with people interested in new reasoning methods and information fusion. So, we hope that this second volume on DSmT will continue to stir up some interests to researchers and engineers working in data fusion and in artificial intelligence....

Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . 6 1.2.2 The conjunctive rule . . . . . . . . . 6 1.2.3 The disjunctive rule . . . . . . . . . 8 1.2.4 Dempster’s rule of combination . . . . . . . 8 1.2.5 Smets’ rule of combination . . . . . . . 9 1.2.6 Yager’s rule of combination . . . . . . . 9 1.2.7 Dubois & Prade’s rule of combination . . . . . . 9 1.2.8 The hybrid DSm rule . . . . . . . . 10 1.3 The general weighted operator (WO) . . . . . . . 11 1.4 The weighted average operator (WAO) . . . . . . . 12 1.4.1 Definition . . . . . . . . . 12 1.4.2 Example for WAO . . . . . . . . . 13 1.4.3 Limitations of WAO . . . . . . . . . 13 1.5 Daniel’s minC rule of combination . . . . . . . 14 1.5.1 Principle of the minC rule . . . . . . . 14 1.5.2 Example for minC . . . . . . . . . 15 1.6 Principle of the PCR rules . . . . . . . . . 20 1.7 The...